After I posted the first message, I called my brother, who had done some family research a few years ago. Adam is indeed the brother of my grandfather, Lawrence (Laurence). He appears in the 1900 Census as Lorenz, son of Hen (Henry) and Margaret. My brother said that Adam appears in the 1870 census as the six-year-old son of Henry and Margaret. The 1900 census says that there were 16 children in all, 10 still living at the time of the census. Lorenz was the only child still living with his parents in 1900 -- he was 17 at the time.
The 1900 census lists Henry's occupation as butcher, which fits with family oral history. He worked out of the stockyards in South Chicago. They were still living in Tinley Park (originally called Bremen or New Bremen). Henry appears in both the 1860 and 1870 census for that area. The 1900 census lists his birthplace as Germany and says that he emigrated in 1852. He was born in 1836, and Margaret was born in 1840. Margaret was also born in Germany, but there is no emigration date.